Using factor theorem factorise $x^{3} - 3 x^{2} - 9 x - 5$

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Solution

$x^{3} - 3 x^{2} - 9 x - 5$
$\Rightarrow x^{2} (x + 1) - 4 x (x + 1) - 5 (x + 1)$
$\Rightarrow (x + 1) (x^{2} - 4 x + 5)$
$\Rightarrow (x + 1) (x^{2} - 5 x + x - 5)$
$\Rightarrow (x + 1) (x (x - 5) + 1 (x - 5))$
$\Rightarrow (x + 1) (x - 5) (x + 1)$
$\Rightarrow (x^{2} - 1) (x - 5)$

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